This PDF file includes:

• Section SA. Choice of null model for the combined effect of multiple independent mutations
• Section SB. Range of validity for population size N
• Section SC. Structural features of fitness landscapes
• Section SD. Relaxation to local fitness maximum
• Section SE. Hopping between MSs
• Section SF. Batch culture
• Fig. S1. Properties of fitness landscape as a function of L.
• Fig. S2. Properties of fitness peaks as a function of L when additional weak interactions
• between all sites are included.
• Fig. S3. Figure showing how properties of MSs vary with fitness for ρ = 0.01 (black diamonds, F_offset = −3.4), ρ = 0.025 (red circles, F_offset = −3.8), ρ = 0.05 (green triangles, F_offset = −4.2), ρ = 0.075 (blue squares, F_offset = −4.4), and ρ = 0.1 (purple crosses, F_offset = −4.5).
• Fig. S4. The number of connecting MSs n_s, which is the number of MSs that the system can transit to next from the current MS, correlates with the number of double mutant escape paths out of a state n_p.
• Fig. S5. Relaxation toward a single local fitness maximum slows down with increasing degree of epistasis.
• Fig. S6. Changing the distribution of fixation probabilities does not significantly change the functional form of the fitness trajectory.
• Fig. S7. Other distributions for the nonzero elements of the interaction matrix give similar form for the fitness trajectory.
• Fig. S8. Logarithmic fitness trajectories are also observed for different values of ρ.
• Fig. S9. The decay of the two-time correlation function depends on both the time difference Δt and the initial time of the measurement t_w, implying that the system ages.
• Reference (45)

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